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中国神经科学学会第十二届全国学术会议

作者： Xinjian Jiang Tenghai Long Stanislas Dehaene Liping Wang Institute of Neuroscience Key Laboratory of Primate Neurobiology CAS Center for Excellence in Brain Science and Intelligence Technology Chinese Academy of Sciences Key laboratory of Brain Functional Genomics Institute of Cognitive Neuroscience School of Psychology and Cognitive Science East China Normal University Collège de France Cognitive Neuroimaging Unit CEA DSV/I2BM INSERM Université Paris Sud Université Paris-Saclay Neuro Spin center

What does seem to be unique to our species in both human languages and expressive power in other domains is hierarchical structure. With this fundamental characteristic, humans are endowed with a finite cognitive computational system that generates infinity of meaningful expressions. This thus has risen to an important question: To what extent does hierarchical syntax deviate from the vocal communication signals of nonhuman animals? It has been proposed that the important distinction between human and non-human animal appears to be between the levels of regular or ‘finite state’ grammars and context-free or ‘phrase structure’ grammars. However, the true grammatical ability in nonhuman animals still remained unclear. Here, we tested three macaque monkeys on a newly designed paradigm: delayed sequence recall task. On each trial the monkeys viewed two（‘A-B’） or three（‘A-B-C’） sequentially presented spatial locations in a sample period, followed by a test period that showing six locations（with three distractors） together. The task was to touch the locations by either repeating（e.g. ‘ABC|ABC’） or reversing（e.g. ‘ABC|CBA’） their original orders without touching distractors. The results showed that all three monkeys successfully learned and generated the sequence defined by a centre-embedding, context-free grammar（mirror structure） and further spontaneously generalized the rule to untrained spatial sequences. These results suggest the context-free grammar is also available to nonhuman animals and probably not uniquely human. Our paradigm should allow us test higher-level of supra-regular grammars in the Chomsky hierarchy and investigate the neural correlates of recursive rules on non-human primates.

关键词： centre-embedding context-free grammar monkey human unique recursion hierarchy

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context-free grammars for Triangular Arrays

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Acta Mathematica Sinica,English Series 2015年第3期31卷 445-455页

作者： Robert X.J.HAO Larry X.W.WANG Harold R.L.YANG Center for Combinatorics LPMC-TJKLC Nankai University

We consider context-free grammars of the form G = {f → f^b1＋b2＋1g^a1＋a2, g → f^b1 g^a1＋1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T（n, k）}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn （x） =∑k=0^n T（n, k）x^k. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn＋1（x） = Pn（Tn（x））. Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br？ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and ***, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.

关键词： context-free grammar stable polynomials real-rootedness Bessel numbers Whitneynumbers

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