Learning the dynamics of embedded clauses

Recent work by Siegelmann has shown that the computational power of recurrent neural networks matches that of Turing Machines. One important implication is that complex language classes (infinite languages with embedded clauses) can be represented in neural networks. Proofs are based on a fractal encoding of states to simulate the memory and operations of stacks. In the present work, it is shown that similar stack-like dynamics can be learned in recurrent neural networks from simple sequence prediction tasks. Two main types of network solutions are found and described qualitatively as dynamical systems: damped oscillation and entangled spiraling around fixed points. The potential and limitations of each solution type are established in terms of generalization on two different context-free languages. Both solution types constitute novel stack implementations - generally in line with Siegelmann's theoretical work - which supply insights into how embedded structures of languages can be handled in analog hardware.

Synthesis and characterization of mono- and bis-ligand zinc(II) and cadmium(II) complexes of the di-2-pyridylketone Schiff base of S-benzyl dithiocarbazate (Hdpksbz) and the X-ray crystal structures of the [Zn(dpksbz)2] and [Cd(dpksbz)NCS]2 complexes

New mono- and bis-chelated zinc(II) and cadmium(II) complexes of formula, [M(dpksbz)NCS] (dpksbz = anionic form of the di-2-pyridylketone Schiff base of S-benzyldithiocarbazate) and [M(dpksbz)(2)] (M = Zn-II, Cd-II) have been prepared and characterized. The structure of the bis-ligand complex, [Zn(dpksbZ)(2)] has been determined by X-ray diffraction. The complex has a distorted octahedral geometry in which the ligands are coordinated to the zinc(II) ion as uninegatively charged tridentate chelates via the thiolate sulfur atoms, the azomethine nitrogen atoms and the pyridine nitrogen atoms. The distortion from a regular octahedral geometry is attributed to the restricted bite angles of the Schiff base ligands. X-ray structural analysis shows that the [Cd(dpksbz)NCS](2) complex is a centrosymmetric dimer in which each of the cadmium(II) ions adopts a five-coordinate, approximately square-pyramidal configuration with the Schiff base acting as a tetradentate chelating agent coordinating a cadmium(II) ion via one of the pyridine nitrogen atoms, the azomethine nitrogen atom and the thiolate sulfur atom; the second pyridine nitrogen atom is coordinated to the other cadmium(II) ion of the dimer. The fifth coordination position around each cadmium(II) is occupied by an N-bonded thiocyanate ligand. (C) 2003 Elsevier Science Ltd. All rights reserved.

The preparation of zinc(II) and cadmium(II) complexes of the pentadentate N3S2 ligand formed from 2,6-diacetylpyridine and S-benzyldithiocarbazate (H2SNNNS) and the X-ray crystal structure of the novel dimeric [Zn2(SNNNS)2] complex

The pentadentate chelating agent, 2,6-diacetylpyridinebis(S-benzyldithiocarbazate) (H2SNNNS) reacts with zinc(II) and cadmium(II) ions forming stable complexes of empirical formula, [M(SNNNS)] (M=Zn2+, Cd2+; SNNNS2 =doubly deprotonated anionic form of the Schiff base). These complexes have been characterized by a variety of physico-chemical techniques. IR and H-1 NMR spectral evidence indicate that the Schiff base coordinates to the zinc(II) and cadmium(II) ions via the pyridine nitrogen atoms, the azomethine nitrogen atoms and the mercaptide sulfur atoms. The crystal and molecular structure of the zinc(II) complex has been determined by X-ray diffraction. The complex is a dimer in which the pyridine nitrogen atom,the azomethine nitrogen atom and the thiolate sulfur atom from one ligand coordinate to one of the zinc(II) ions whereas the azomethine and thiolate sulfur atoms from another ligand complete pentacoordination around the zinc(II) ion, the ligands being coordinated in their deprotonated forms. The coordination geometry about each zinc(II) can be considered as intermediate between a square-pyramid and trigonal-bipyramid. The cadmium(II) complex is also assigned with a dimeric structure. (C) 2003 Elsevier Ltd. All rights reserved.