spontaneous symmetry breaking transitions can occur which we will use was ...... calculate the probability distribution function (PDF) for such a flow, we follow ...
spontaneous symmetry breaking, many of which will be discussed in more detail by other lecturers, and discuss their general features. The second lecture will ...
Dec 5, 2017 - possible that combinatorial complexity mathematics could be applied as a ..... http://three-body.ipb.ac.rs/ref.php. 19. Weyl H. Symmetry.
by Nambu and Goldstone.1,2 One of consequences of SSB is the presence of ... Thus it avoids both the massless Goldstone bosons and the massless.
and references therein. Its significance lies in its simple. ''typical form'' which appears in many applications. Indeed, the unperturbed Duffing oscillator represents ...
Goldstone's theorem, in its usual context, determines zero eigenvalues of the mass matrix for ..... This is Goldstone's theorem that we shall shortly prove formally ...
Poisson-Boltzmann problem, attraction between identical surfaces. 1. Introduction .... carried out with the classical Derjaguin formula- tion. We scale the normal ...
Abstract. We study a model Dyson-Schwinger equation for the quark propagator closed using an Ansatz for the gluon propagator of the form D(q) â¼ q2/[(q2. ).
Netzwerk fÃ¼r genÃ¼gend lange Zeit gegenseitig auf zuverlÃ¤ssige SchÃ¤tz- werte ihrer ...... 1Mica 2, Texas Instruments CC1000, focus.ti.com/lit/ds/symlink/cc1000.pdf ...... 8.1. OPTIMAL SYMMETRIC ALGORITHM. 101 the number of bins receiving exactly l
In this and the following chapter, we discuss the case of spontaneous symmetry breaking, first in general and then applied to the ... through the potential barrier. In field theory, such tunnelling can ..... We represent the charge operator as the vo
We show experimentally that performing symmetry breaking with only a subset of all symmetries can ... sented a method of dynamic symmetry breaking which could deal with large groups of ..... grid of n2 coloured squares6. By clicking on any ...
It is easy to expand around these saddle points to discover asymptotic expansions for each ...... While we were too innocent in our slowness to publish and.
Jun 8, 2009 - the flavour symmetry is broken by the Yukawa couplings to the Higgs boson, and ..... minimal flavour violation (or beyond ), the dynamics of ...
that instantons can induce supersymmetry breaking in models in 0 + 1 dimensions .... 2), exhibits the pole characteristic of spontaneous symmetry breaking.
Apr 16, 1998 - as follows: Suppose that Professor X is blind and has a circular key ring with seemingly ... If G is a graph, then a symmetry or automorphism of G is a ... To see that Ï is an automorphism of G1, notice that the images of all ..... ha
Dec 13, 2017 - To cite this article: Hiroyuki Abe et al JHEP11(2007)044. View the ... Published by Institute of Physics Publishing for SISSA .... First, we review briefly the argument by Nelson and Seiberg  in ... Therefore, there is no SUSY solut
Mammalian oocyte meiosis encompasses two rounds of asymmetric div- isions to generate a totipotent haploid egg and, as by-products, two small polar bodies.
exothermic chemical reaction fuels the pattern-formation through a coupling of Marangoni and .... velocities were measured using the motion analysis macro of the Bioscan software which uses Microsoft. Excel 4.0 for statistical analysis.
Aug 19, 2005 - materials featuring colossal magnetoresistance, and shows ... dence of the dielectric constant of the two samples which we studied confirmed ...
models the problem successfully, but in practice search is prohibitive. We need .... 'first', 'second', ..., 'nth' compounds in a column, as defined in the previous section, ascending. We denote .... 0 10 1 9 2 8 3 7 4 6 5. 3 7 4 6 5 0 10 1 9 2 8 ...
SPONTANEOUS SYMMETRY BREAKING PHENOMENA. WITH NON-EQUIVALENT VACUA. N. C. Bobillo-Ares. Departamento de Matemticas. Facultad de ...
techniquarks (UTC,DTC)r,b,g plus a doublet of technileptons (NTC,ETC) are severely ...... then result in both the right-handed technineutrinos NTC. R ...... (111) leading to resonances in R. The techniomega Ï0. TC being associated with the isosingle
Sep 16, 2009 - mechanisms that govern cellular symmetry breaking during animal development. Here we focus on two ... the C. elegans zygote (called P0) dates back to .... WHAT IS THE CUE? ..... Establishment of apico-basal Par asymmetries on somatic b
on a PowerPC 1GHz G4 processor with 1.25 GB RAM. n by n queens. As in the .... 440. 100. 5483. 0.04. 303. 100. 5305. 0.05. S(15, 4). 168. 6976512. 93094291.
Morphological Variation, Symmetry Breaking and Reduction of Complexity 4th Lecture Anna Maria Di Sciullo UQAM Morphology Fest Symposium on Morphological Complexity Bloomington June 16-20, 2014 This work is supported in part by funding from the Social Sciences and Humanities Research Council of Canada to the Major Collaborative Research on Interface Asymmetries, grant number 214-20031003, and by funding from the FQRSC on Dynamic Interfaces, grant number 137253. www.interfaceasymmetry.uqam.ca. www.biolinguistics.uqam.ca
Outline 1. 2. 3. 4.
Diachrony and morpho-syntactic complexity Models of language development and change Symmetry breaking and the development of P Complexity reduction in phylogeny
Diachrony and morpho-syntactic complexity
The language faculty is stable. Languages vary because of contact with the environment. The variation is the consequence of a change in the properties of features. Diachronic variation is gradual and it may bring about morphological complexity giving rise to differences in the form and in the distribution of morphological elements (prepositions, postpositions, adpositions, circumpositions). We will discuss diachronic evidence from Indo-European languages showing that symmetry breaking reduces the complexity that arises in the development of functional elements. See Di Sciullo (2014) for further discussion. (1) [Quniv . . . [Dem . . . [Numord . . . [RC . . . [Numcard . . . [Cl . . . [A . . .NP]]]]]]] (Cinque 2005) (2) CPlace - DegPlace - Place - Ploc - DP (den Dikken, to appear, Koopman 2000) (3) p - Deg - Deix - Loc - AxPart - K – DP between -near- besides (Svenonius 2013)
Three cases – multi-functional -esimo – supplementary a– unstable cum/co
1.1 -esimo The multi functional –esimo diachronic development. From Latin –esimus (masc.) gave rise to the –esimo (It) –ième (Fr) in ordinals, e.g. ventesimo (It), vingtième (Fr) In Vulgar Latin metipsimus is formed of met (ego), ipse (self focus) and -issimus (superlative). The Roman-Latin medisme gave rise to medesimo in Italian, meïsme and mesme in Old French, to mismo in Spanish and to mesmo in Portuguese. (4) Numord -esimus
From Latin –esimo (identical form in masc. and fem.) derived complex N from N: protestante , protestantesimo
-esimo in ordinal numbers Language variation -Cardinals Lexical numbers and complex numerals
-Ordinals Based lexical / complex numerals Based on complex numerals .
Ordinals in Italian In Italian, the merger of -esimo with a complex cardinal yields an ordinal number. undic-esimo, ….vent-esimo , … mill-esimo, … million-esimo, …. Si tratta dell'ennesimo dramma di una lunga serie. ‘It is the umpteenth drama in a long series.’
-esimo in adjectives The merger of esimo with med yields an emphatic identity adjective, as the examples in (5)-(8) illustrate.
(5) medesimo, medesima, medesimi ‘same sg’,‘same fem sing’, same pl’ (6) Mi ha detto le medesime cose. ‘He told me the same things.’ N (7) Il presidente medesimo era presente ‘The president EMPHATIC was present.’ (8) Il presidente era il medesimo. ‘The president was the same one.’
Ordinal numbers and adjectives in Italian The ordinal number, the adjective and the pronoun have a binary branching structure and include a multifunctional affix structure
1.2 Supplementary a in Italian There is variation in the pronunciation of the preposition a ‘at’ in functional words denoting locations and directions in Italian dialects, including Fallese, a dialect spoken in Abruzzi (Catinella, 1998) and Piemontese. The supplementary a in Fallese is a morphological remnant of Latin ad/ab PP structures. Not present in Italian. (9) a. addo (Fa) b. dove (It) ‘where’
(10) a. *achi (Fa) ‘who’ b. *ache ‘what’ c. *aquale ‘which’ d. *aquand ‘when’ e. *aquant ‘how much’ f. *apeche ‘why’
Locative prepositions In Latin, when a complement expresses not the place itself but the proximity of a place or a person, it is preceded by a preposition, ab, ad, or apud ‘to, toward, near’. In Fallese the prefix a- is part of complex prepositions, whereas this is not the case for their Italian (It) counterparts, (11)-(12). This suggests that supplementary a- in Fallese could be the remnant of the Latin locational preposition ad. (11) a. ammonde (Fa) b. ad montem (Lat) at hill ‘upward’ c. in salita (It) (12) a. abballe (Fa) b. ad vallem (Lat) at valley ‘downward’ c. in basso (It)
Other functional categories Supplementary a- in functional categories other than prepositions, wh-words, deictic determiners, adverbs: (13) WH-P a. addo (Fa) b. ad ubi (Lat) c. dove (It) at where ‘where’ b. aqquande (Ar) b. ad quando (Lat) c. quando (It) at when ‘when’ (14) DEM a. aecche (Fa) b. ad ecce (Lat) c. qui (It) at here ‘here’ b. aell b. ad illic c. li (It) at there ‘there’ (15) ADV a. accusci (Fa) b. eccu sic (Lat) c. cosi (It) it is so ‘thus’ b. allore b. ad hora(m) c. allora (It) at this ‘then’
Other dialects Supplementary a- is expected to be found in other dialects in similar strutures This is the case in Piemontese (Brero 1975, Gribaud 1983) (16) Wh-P ando (Pie) ‘where’ (17) PP abass (Pie) ‘down’ (18) Adv ancheuj (Pie) ‘today’
in basso (It) abbasso (Fa)
en bas (Fr)
Complexity reduction: Minimize externalization (SM) pronounce the minimum
1.3 Comitative co - pronominal complement
Latin is prepositional, Old Italian is also postpositional and circumpositional, Modern Italian is prepositional: cum me, me cum, meco, con meco, con esso meco, con me, as evidenced in Di Sciullo, Nicolis & Somesfalean (2014). We proposed an account of the diachonic change in terms of the interaction of the computational procedure of the language faculty with principles reducing complexity: Directional Asymmetry Principle (DAP). Language development is symmetry breaking. (Di Sciullo 2011)
The P shell We proposed an account for this variation in terms of a P-Shell structure, which we take to be the minimal structure for functional categories, as in Di Sciullo (2000, 2005). The lower and the higher heads of the P-Shell host formal features, valued features as well as unvalued features, including Case features. The pronominal complement may occupy different position in the P-Shell, linked to the sister of the lower P head.
cum me, me cum, meco, con meco, con esso meco, con me 1 ,1 ,1 ,2 , 3 ,1 Latin__ ____________ Old Italian ______________ Modern Italian
Explaining the phenomenon Diachronic changes can be explained in terms of the interaction of the grammar internal pressure imposed by the initial position of the P head, on the one hand, and, on the other hand, by principles of efficient computation. Complexity may arise from experience (language acquisition, language contact, pragmatic factors, etc.) giving rise to choice points (symmetry) in functional feature structure, with the consequences of enlarging the set of possible derivations. Principles of parsimony, falling into the third factor, will eliminate the complexity by breaking the symmetry brought about by experience. Principles of efficiency are deep rooted in the human cognitive system and act as soon as possible in language acquisition. Their effects are however gradual in language diachronic development, as environmental dynamics is not deterministically driven by genetic determinism.
Directional Asymmetry Principle Evolutionary developmental universals emerge in language historical development in terms of the Directional Asymmetry Principle (DAP). According to the DAP, Language development is symmetry breaking. (Di Sciullo 2011) The DAP targets properties of relations, (33), between features, (34), and structures, (35). (33) R(a,b) & R(b,a) -> R(a,b) (34) Valued/Unvalued Feature Constraint (V/UFC) In a functional feature structure F, [F [F][uF] ], where [F] and [uF] are symmetrical with respect to F, the symmetry will tend to be broken in language development. (35) Head Initial⁄Final Constraint (HI/FC) In a configuration [X X YP], where X is a head and YP is its complement, if both < X, YP > and < YP, X > are possible SM linearizations, only one linearization will tend to survive in language development. The DAP is not a global principle on the development of languages. It is a local principle applying to micro feature structures within languages, for example the fluctuation in the position of the pronominal complement wit respect to its comitative prepositional head. Once the asymmetrical stage it attained in a given micro structure, symmetry may reappear within that micro structure. The DAP predicts that the symmetry will gradually be eliminated. See Di Sciullo 2011-2013; Di Sciullo & Nicolis 2012; Di Sciullo & Somesfalean 2013; Di Sciullo, Nicolis and Somesfalean 2014 for discussion.
The DAP and the Models of language variation Macro parameters Minimalism and micro parameters Phylogenetic stable states Phylogenetic dynamic states
Principles and Parameters Model Parameter : option left open in the principles of UG Macro parameters -Head directionality parameter -Pro-drop parameter -Bounding nodes -Polysynthesis parameter
Open questions -Are there restrictions on possible parameters? (limited set?) -Are all parameters binary? How many are there? -Which parameter setting algorithm is correct? -Are there any biological correlates?
Minimalist program (Merge and the computational procedure of feature valuing) Parameters reduce to abstract properties (features) of functional elements Unified approach to variation between languages and dialects Demonstratives (Dem) are universally generated in a ‘low area’ of the DP (D Gen1 Adjs Dem Gen2 NP) and different movements (parameter 1- 4) derive the different positions of Dem cross-linguistically (Longobardi and Guardiano 2009)
Par 1: - Strong deixis (Dem moves to Spec DP to check deixis) Par 2: - Strong locality (Dem moves to Spec DP to check deixis and locality) Par 3: - DP over Dem (Dem moves to the Spec DP, DP moves to its left periphery) Par 4: - D(person)-licensing Dem (Dem and the article never co-occur in Spec DP)
Phylogenetics Based on lexical properties (Gray and Atkinson 2003; Pagel, Atkinson, and Meade 2007) Language taxonomy based on word cognates. Based on abstract syntactic properties (Longobardi and Guardiano 2009) Parametric syntax serves phylogenetic purposes better than lexical methods. Languages and dialects are more closely related than what it might appear from the classifications based on lexical items.
Phylogenetics stable /dynamic states Based on stable states Languages with dominant VSO order are always prepositional. With overwhelmingly greater than chance frequency, languages with normal SOV order are postpositional. (Greenberg’s Universals) Based on dynamic states Language variation is symmetry breaking Di Sciullo 2011, 2012; Di Sciullo & Nicolis 2012; Di Sciullo & Somesfalean 2013; Di Sciullo, Nicolis & Somesfalean 2014. (A)symmetry based syntax serves phylogenetics purposes from a dynamic viewpoint. Symmetry-breaking comparison method displays the advantages of phase transition dynamics. Languages and dialects are more closely related than what it might appear from the classifications based on stable states.
Symmetry, antisymmetry, asymmetry Properties of relations, including symmetry and asymmetry are used in biology, physics and linguistics to describe the properties and the dynamics of natural systems. In linguistics, properties of relations have been shown to contribute to our understanding of linguistic phenomena. Kayne 1994, The Antisymmetry of syntax (a) (LCA: c-command and linearization) Moro 2000, Dynamic Antisymmetry (b) (symmetry breaking and displacement) Di Sciullo 2005, The Asymmetry of Morphology (c) (asymmetry and preservation)
Biology Symmetry breaking, which may occur at multiple levels, is a prevalent process in biology, because organismal survival depends critically on well-defined structures and patterns at both microscopic and macroscopic scales. Symmetry breaking at the sub-cellular level can lead to the establishment of a persistent for such processes as cell division, cell fusion, and axon specification. Symmetry breaking is a result of the interplay between the system dynamics and the internal or external cues that initiate and/or orient the eventual outcome. (Thompson 1942).
Evolutionary developmental biology In evolutionary developmental biology, symmetry-breaking is a core aspect of evolution and change in different species (Graham, Freeman & Emlen 1999; Palmer 1996, 2004; Palmer & Lowentin 2004). Phylogenetic patterns of variance in the evolution of bilateral asymmetric species : Symmetry > fluctuating asymmetry > directional asymmetry (Palmer)
Development & evolution of claw asymmetry in fiddler crabs (Uca) Phenotype-leads mode of evolution (genetic assimilation) Palmer (Science 2004, Current Biology 2009)
Summary of Part 2
• • •
Computational procedure of the LFN + experience + Factors reducing complexity Open questions in our understanding of language variation The DAP and dynamic models of phylogeny
3. Predictions DAP and the development of P Two predictions of the DAP developmental constraint: A: Stable state / Directional asymmetry should be synchronically widespread. B: Oscillation / Fluctuating asymmetry should characterize older diachronic stages. Both predictions are borne out for the development of P and its DP complement. (Di Sciullo 2012, 2013; Di Sciullo and Nicolis 2012)
Prediction A for P Stable state / Directional asymmetry should be synchronically widespread (Di Sciullo & Nicolis 2012)
The predictions A and B are validated on a number of languages closely related to Proto-Indo-European .
Prediction B for P: Fluctuation should characterize older diachronic stages (Di Sciullo & Nicolis 2012)
Summary The predictions A and B for our hypothesis for the development of P are validated on a number of languages closely related to Proto-IndoEuropean. The diachronic development of languages displays a phase of fluctuation where a complement may precede or follow its P head; this is true even for languages which display a clear preponderance of prepositions or postpositions. (Hewson and Bubenik 2006; Friedrich 1975). As evidenced in Di Sciullo & Nicolis (2012), there is a clear diachronic tendency towards the gradual elimination of a fluctuating state and the development of a stable state, in the Indo-European diachrony: Homeric Greek > Classical Greek > Modern Greek Latin > Umbrian > Old Italian > Modern Italian Old English > Early Modern English > Modern English
4. Complexity reduction in phylogeny
Why would there be a bias favoring prepositions instead of postpositions in the diachronic development of P in the languages under consideration?
Pre-positions and postpositions The fluctuation between pre- and post- nominal positions wrt a functional head may follow from the availability of both a valued and an unvalued [D] feature for the functional heads F and P dominating D. Only the [uD] feature of F is checked in the case of prepositions, whereas the [uD] feature of P would also be checked in the case of post-positions.
Factors reducing complexity Principles external to the Language Faculty Part of other cognitive systems of the brain / natural world Derivational: Reducing the computational load Shortest derivation (Kolmogorov 1965) Fodor, Bever & Garrett (1974) Limiting the search space Derivation by phases, Minimal search, etc. (Chomsky 2000, 2005, 2008) Representational: Reducing the computational load of the interfaces Pronounce the minimum (SM) (Chomsky 2011) Syntax-semantic transparency thesis (CI) (Chierchia 1985) Limiting the set of possible acquirable grammars and language variation (Yang 2002, Niyogi 2006, Niyogi and Berwick 2009) Dynamics of complex systems: Symmetry breaking in phylogeny (DAP) (Di Sciullo 2011-2013)
Summary We proposed a developmental universal relying on symmetry-breaking and tested its empirical predictions. As predicted a fluctuating symmetry (choice point) can be observed in the diachrony of the languages in consideration and tends to be gradually reduced. Generally, the surviving derivations are shorter than the ones that were eliminated. This brings further justification to the hypothesis that symmetry breaking is part of the factors reducing complexity.
Further questions Most languages go through a stage of fluctuation. Most predominantly prepositional languages remained prepositional after the fluctuation (Greek, Latin, Germanic). Some predominantly postpositional became prepositional after fluctuation (Persian)
Why is it the case that the fluctuation is still ongoing in some languages? (Russian, Chinese, Pashto)
Why are there languages with postpositions at all? (Hittite, Hindi)
Questions A and B A) Why is it the case that the fluctuation is still ongoing in some languages ((Russian, Chinese, Pashto) ? Notice that this does not goes against our theory, which does not treat fluctuating asymmetry as banned by grammar, but rather considers it computationally more costly than directional asymmetry. What we predict is that a switch from fluctuating to directional asymmetry is complexity reducing and thus likely to happen. To exemplify, consider the possibility of expressing the notion of movement along a path by means of either a postposition ta “for” or a preposition pә “by”. a. …melma to b. pә lār (Pashto) guests for by road “[they are preserving X] for the guests” “by the road” B) Why are there languages with postpositions at all? Some predominantly postpositional languages remained postpositional after fluctuation (Hindi). Why is this the case ? Greenberg’s Universal no 4: languages with normal SOV order are postpositional.(e.g. Hindi, Turkish, Finnish, Hindi, Korean, Hungarian), and VSO languages are always prepositional (Welsh, Classical Arabic, Tagalog). Middle-Late-New Hittite (14th-13th c BC) Middle and Late Hittite are consistently post-positional. For example, while andan (‘inside’) can be used both pre- or post-positionally in Old Hittite, it becomes exclusively post-positional in New Hittite, (18), (H&B p.96). [ﾌD-i anda ]lāhuwai (NH) River-dat/loc into pour-3sg ‘’she pours into the river’’ In SOV language, Object Shift in PP (Bošković 2004) would not be costly because it is required independently.
Selected references Anderson, P.W. 1972. More Is Different. Science Vol. 177 no. 4047 pp. 393-396. Biberauer, T., A. Holmberg & I. Roberts 2010. A Syntactic Universal and its Consequences. Ms. University of Cambridge. Bošković, Ž. 2004. 'Object shift and the clause/PP parallelism hypothesis', Proceedings of the. West Coast Conference on Formal Linguistics 23, 99-112. Cinque, G. 2005. Deriving Greenberg’s Universal 20 and its exceptions.Linguistic Inquiry 36 3: 315–332. | Chomsky, N. 1995. The Minimalist Program. Cambridge Mass: MIT Press. Chomsky, N. 2005. Three Factors in Language Design. Linguistic Inquiry 36:1–22. Di Sciullo, A.M. 2014. Economy and multifunctional affixes. 16th International Morphology Conference. Budapest. Di Sciullo, A.M. 2013. Language Faculty, Complexity Reduction and Symmetry Breaking. In Marc Richards (ed.), GLOW Newsletter 70. Di Sciullo, A.M. 2012. An Evolutionary Developmental Constraint. Department of Linguistics and Philosophy. MIT LingLunch talk. Di Sciullo, A.M. 2011. A Biolinguistic Approach to Variation. In A.M. Di Sciullo ad C. Boeckx (eds.) The biolinguistic Entreprise: New Perspectives on the Evolution and Nature of the Human Language Faculty, p. 305-328. Oxford : Oxford University Press. Di Sciullo, A.M. 2005. Asymmetry in Morphology. Cambridge. Mass: The MIT Press. Di Sciullo, A.M., M. Nicolis & S. Somesfalean. Forthcoming 2014. Comitative P. In J. Garzonio & S. Rossi (eds.). Variation in Prepositions. Oxford Studies in Comparative Syntax. Oxford University Press. Di Sciullo, A.M. & S. Somesfalean. 2013. Variation in the Position of the Definite Determiner in Romanian: A Biolinguistic Perspective. Romance Linguistics in the Pacific: Variation in Time and Space. Special Issue of the Australian Journal of Linguistics 33(2): 121-139. Taylor & Francis. Di Sciullo, A.M. & M. Nicolis 2012. Third Factor in the Development of P. North East Linguistic Society 42.
Selected references Djamouri, R., P. Waltraud and J. Whitman. 2011. Postpositions vs. Prepositions in Mandarin Chinese: The Articulation of Disharmony, Theoretical Approaches to Disharmonic Word Orders, ed. by T. Biberauer and M. Sheehan, Oxford University Press. Fortson IV, B.W. 2010. Reconsidering the History of Latin and Sabellic Adpositional Morphosyntax. American Journal of Philology 131:121-154. Gallistel, C.R. 1990. The Organization of Learning. Cambridge Mass: MIT Press. Giusti, G. 1993. La sintassi dei determinanti. Padova. UniPress. |Greenberg, J. 1966. Language Universals: With Special Reference to Feature Hierarchies. The Hague: Mouton. Greenberg, J. 1966. The Universals of Language. Cambridge, Mass: MIT Press. 1963. Gray, R. D. and Q D. Atkinson. 2003. Language-tree divergence times support the Anatolian theory of Indo-European origin. Nature, 426(6965):435--439. Hewson, J. and V. Bubenik 2006. From Case to Adpositions. The development of configurational syntax in Indo-European languages John Benjamins Publishing Kayne, R. 1994. The Antisymmetry of Syntax. Cambridge. Mass: The MIT Press. Kayne, R. 2011. Why are There No Directionality Parameters ?. In M Byram Washburn et al (ed) Proceedings of the 28th West Coast Conference on Formal Linguistics. Somerville: Cascadilla. Pp. 1-23. Longobardi G. and C. Guardiano. 2009. Evidence for Syntax as a Signal of Historical Relatedness. Lingua, 119, 11, 16791706. Moro, A. 2000. Dynamic Antisymmetry. Cambridge. Mass: The MIT Press. Niyogi, P. 2006. The Computational Nature of Language Learning and Evolution. Cambridge, Mass: MIT Press. Niyogi, P. and R. Berwick 2009. The proper treatment of language acquisition and change in a population setting. Pagel, M., Atkinson, Q., Meade, A., 2007 .Frequency of word-use predicts rates of lexical evolution throughout IndoEuropean history. Nature 449, 717 - 720 Palmer, A.R. 2004. Symmetry Breaking and the Evolution of Development. Science 306:828-833. Wexler, K. 1998. Very early parameter setting and the unique checking constraint: A new explanation of the optional infinitive stage. Lingua 106: 23-79. Yang, C. 2002. Knowledge and Learning in Natural Language. New York: Oxford University Press.
Morphology and Computation Recapitulation of the Lectures Minimalism and I-morphology composition & recursion based on asymmetrical relations, structure and features derivation, exocentric compounds, complex numerals Exploring asymmetry effects in I-morphology Processing asymmetric relations argument/adjunct asymmetry in deverbal compounds internal/external aspect asymmetry in prefixed verbs Two approaches to morphological complexity I-complexity ≠ E-complexity behavioral and computational linguistic results derivational morphology, compounds Morphological variation, symmetry breaking and reduction of complexity language diachronic morpho-syntactic complexity the DAP and the development of prepositions in phylogeny Principles reducing complexity: Minimize symmetry Minimize externalization