A Systemic-Dynamic Lurian Approach to Aphasia in Bilingual Speakers

For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, there are very good estimates of the largest constraint density for which solutions exist. Yet, all known polynomial-time algorithms for these problems fail to find solutions even at much lower densities. To understand the origin of this gap we study how the structure of the space of solutions evolves in such problems as constraints are added. In particular, we prove that much before solutions disappear, they organize into an exponential number of clusters, each of which is relatively small and far apart from all other clusters. Moreover, inside each cluster most variables are frozen, i.e., take only one value. The existence of such frozen variables gives a satisfying intuitive explanation for the failure of the polynomial-time algorithms analyzed so far. At the same time, our results establish rigorously one of the two main hypotheses underlying Survey Propagation, a heuristic introduced by physicists in recent years that appears to perform extraordinarily well on random constraint satisfaction problems.

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“…Since the property "has more than q satisfying assignments" has a sharp threshold [13], this assertion implies that for every…”

Section: Establishing Exponentially Many Clustersmentioning

confidence: 94%

On the solution-space geometry of random constraint satisfaction problems

Achlioptas

Ricci-Tersenghi

2006

Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing

110

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“…Taking t = E[X]/poly(n), implies that X is within a polynomial factor of its expectation Λ b (1/2, k, r) n/2 , also with constant probability. Since the property "has more than q satisfying assignments" has a sharp threshold [11], this assertion implies that for every r < 2 k ln 2 − k, w.h.p.…”

Section: In [4] It Was Shown That E[x]mentioning

confidence: 93%

Solution clustering in random satisfiability

Achlioptas

2008

Eur. Phys. J. B

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Abstract. For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, we have very good estimates of the largest constraint density for which solutions exist. All known polynomial-time algorithms for these problems, though, already fail to find solutions at much lower densities. To understand the origin of this gap we study how the structure of the space of solutions evolves in such problems as constraints are added. In particular, we show that for k ≥ 8, much before solutions disappear, they organize into an exponential number of clusters, each of which is relatively small and far apart from all other clusters. Moreover, inside each cluster most variables are frozen, i.e., take only one value.PACS. 02.50.-r Probability theory, stochastic processes, and statistics -75.10.Nr Spin-glass and other random models

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“…Soon afterward, we encountered a similar case in which once more the vernacular was more disturbed than the foreign language, leading to the formulation of a systemic-dynamic interpretation of bilingual aphasia (Kotik, 1979(Kotik, , 1984(Kotik, , 1992(Kotik, , 1996(Kotik, , 2001. For the development of this model, the concept of "extracortical organization of mental functions" is especially important.…”

Section: Cross-cultural and Neuropsychological Analysis Of Higher Menmentioning

confidence: 99%

“…This means that learning to read in one's first language may affect the functional lateral organization of the brain. A constellation of various potentially possible factors relevant to the process of bilingual development that can influence the brain organization of languages is presented in a recent paper (Kotik-Friedgut, 2001). …”

Section: Cross-cultural and Neuropsychological Analysis Of Higher Menmentioning

confidence: 99%

“…Attempts at generalization and systematization of bilingual aphasia started from monofactorial hypotheses, and only later were various lists of factors considered (for review see Kotik-Friedgut, 2001). The systemic-dynamic approach in the analysis of the brain organization of higher mental functions rejects any attempt to interpret aphasic symptoms in bilinguals, or any neuropsychological problem, as stemming from any single factor, and offers an alternative explanation.…”

Section: Cross-cultural and Neuropsychological Analysis Of Higher Menmentioning

confidence: 99%

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Development of the Lurian Approach: A Cultural Neurolinguistic Perspective

Kotik-Friedgut¹

2006

Neuropsychol Rev

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This article presents a discussion of the principle of extracortical organization of higher mental functions and its significance for the development of contemporary neuropsychology. The role of external factors (stimulus-mediator, symbol) in establishing functional connections between various brain systems is, in principle, universal. However, inasmuch as differing mediators and means, or significantly different details within them (direction of writing, orientation by maps or by the behavior of sea birds, etc.) may and in fact do develop in different cultures, neuropsychological analysis must take into account cross-cultural differences. Diagnostic tools must also be adapted to differing cultural contexts. The efficacy of this principle for the analysis of bilingual aphasia and of mental organization of speech, including the effect of acquisition of literacy in native language, is demonstrated. The importance of this principle for the development of new directions in applied neuropsychology is also discussed.

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A Systemic-Dynamic Lurian Approach to Aphasia in Bilingual Speakers

Cited by 17 publications

References 31 publications

On the solution-space geometry of random constraint satisfaction problems

On the solution-space geometry of random constraint satisfaction problems

Solution clustering in random satisfiability

Development of the Lurian Approach: A Cultural Neurolinguistic Perspective

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