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Linguistic Capacity: Associative or Combinatory? Chomskyan models of natural-language grammars, based on formal language theory, crucially rely on the assumption that linguistic knowledge contains two different components, namely, one combinatory system syntax and one that contains knowledge about the use of elementary building blocks lexicon. Post-Chomskyan theories of grammar in particular, Construction Grammar posits that words and syntactic structures and whatever is in between must be treated in a homogeneous manner, since they are all alike in that they consist in associations of formal properties with semantic ones.

In accordance with this, constructionism says we do not use linearly ordered sequences consisting of lexical building blocks in linguistic communication, but complex and possibly overlapping patterns constructions arising from the simultaneous satisfaction of various constraints.

Mindmaker Ltd. In this implementation, constructions constitute a network, and they activate each other through associations. Yet, each carries essentially symbolic information, and the task is essentially combinatory.

New Trends in Formal Languages

It is unclear for the moment how familiar sub-symbolic representation and learning systems e. The long-awaited book of Stephen Wolfram has been completed. This massive, page tome is a great intellectual achievement: one of his friends suggested it should be called PrincipiaComputatus.

Using the early results of his investigations into the behaviours of cellular automata, and the technical computing system Mathematica he created, the book presents a huge number of examples of various scientific disciplines where simple rules generate immensely complex results. The book culminates in the Principle of Computational Equivalence implying that at some level of complexity everything is exactly as complex as anything else. A New Kind of Science is a readable book sharing his ideas with scientists and also with nonscientists. Throughout the book, emphasis is placed on the algorithm rather than the equation.

Wolfram predicts it will have unprecedented implications for science and scientific thinking. Understanding the function of the prefrontal cortex PFC is crucial to reveal the biological mechanisms of thought— and mood disorders and it is also a central question in cognitive neuroscience. It is widely accepted that PFC plays essential role in working memory, especially in executive functions, a main component of working memory. From neurobiological perspective the function of working memory is maintaining neural representations of different kind of sensory or learned information temporally in activated form for on-line processing.

Manipulation of this information held in working memory by executive functions is a necessary step to goal directed behavior. A characteristic feature of neuronal activity in the PFC is the vigorous response in tasks requiring short term retention of information, like delay response tasks. Disturbance of this activity results in faulty behavioral responses indicating its central role in normal functions as well as clinical symptoms.

It is reasonable to assume that optimal regulation of delay-related activity is essential for flexible and at the same time accurate behavior. Accordingly, irresistible activity or instability of it could result in perseveration or distractibility, respectively, which are characteristic symptoms of prefrontal dysfunction. The original idea about the neuronal mechanisms underlying delay-related activity was that reverberation of activity between interconnected neurons.

However, this mechanistic proposal has a limited explanatory power considering the diversity of circuits integrated in the PFC. The purpose of this talk is to give an introduction about the state of our knowledge regarding on the organizational principles of these cortical and subcortical networks whose activities are needed to be integrated in a comprehensive model of the PFC. An overview is given about the Neural Networks, the recently developed, but not yet released application of Mathematica.

The most significant feature of this package, that the symbolic form of a trained network can be produced, consequently it is an easy job to implement it into other applications. Examples from different fields of sciences will demonstrate the usage of the different type of networks, which are available in the Neural Networks application. Experiments have in number theory a long tradition, although they were called rather as examination of tables or numerical test of conjectures.

Both Gauss and Riemann did thorough numerical investigations with "pencil on paper" before stating the conjectures.

In the 20th century because of the idea of computers and the development of the algorithmic point of view more and more researcher were interested for the representation of mathematical objects and algorithmic aspects of operations. The investigations of Derek and Emma Lehmer, Zassenhaus and Cassels means a transition from the precomputer to the computer age. They belong to those scientists, who realized that computers may become experimental facilities for mathematics.

One of the most important results of the beginning, i. It was stated again after long and careful numerical tests, but this time the tests were done by computers. The solution of diophantine equations is an interesting branch of number theory since ancient ages. A systematic theory exists only since the beginning of the 20th century, by our opinion since the talk of Hilbert at the 2nd Conference of Mathematicians in Paris, In Debrecen investigations started in this directions in the early 80th.

We developed algorithms among others for the solution of Thue-, index form- and elliptic equations, implemented and applied them for large sets of input data. Roy, N. Nucleic Acids Res. Espel, E. Cell Dev. Leppek, K. Roquin promotes constitutive mRNA decay via a conserved class of stem-loop recognition motifs. Meister, G. Cell 15 , — Yang, L. Genomewide characterization of non-polyadenylated RNAs.

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Dr Sergey Kitaev | University of Strathclyde

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