Book Review: Nonlinear Dynamics and Chaos: Where Do We Go From Here? Edited by S. J. Hogan,A. R. Champneys,B. Krauskopf,M. di Bernardo,R. E. Wilson,H. M. Osinga,and M. E. Homer. Institute of Physics Publishing,Bristol, 2002, 358 p. ISBN 0-7503-0862-1

Nonlinear Dynamics, Psychology, and Life Sciences -     

Simplified enrichment and identification of environmental peptide toxins using antibody-capture surfaces with subsequent mass spectrometry detection

The development of a simplified assay for detection of congeners of the microcystin (MC) hepatotoxin is described that combines the extreme sensitivity of surface-enhanced laser desorption/ionization time-of-flight MS (SELDI TOF-MS) with the superior selectivity of immunoaffinity interactions. Using methods similar to those of conventional immunoassays, MC standards were captured and enriched on immunoreactive ProteinChips coated with an MC-antibody and analyzed by TOF-MS. Unlike with conventional immunoassays, individual congeners were resolved from mixed pools. Assay conditions were optimized for the quantification of MC from untreated raw pond water at concentrations as low as 0.025 microg L(-1), well below the public health relevant guideline of 1 microg L(-1).     

On the sign of magnetic anisotropy and electronic structure of ferrous ammonium sulphate hexahydrate

The magnetic anisotropies and principal susceptibilities of ferrous ammonium sulphate hexahydrate are investigated to remove the existing discrepancies in the sign of its molecular magnetic anisotropy and the nature of ligand field and electronic structure.     

Effects of Random Noise and Internal Delay in Nonlinear Psychophysics

The effects of introducing second-order random noise on to parameters, so that they are unstable over time, and the effects of internal delay in a deterministic and therefore noise-free recursion are compared. This is done by examining changes in the shape of the escarpment region which corresponds to the traditional psychometric function in sensation intensity or threshold experiments. Some of the grosser psychophysical response surface features are preserved, but only over a limited region of the parameter space. The system is robust against low noise and very brief internal delays, but will lose information and stability outside the region corresponding to low inputs and medium stability. This finding is compatible with what is reported on nonlinear cellular neural networks, for which a few analytical results on stability have been derived.     

A Series of Rare-Earth Mesoionic Carbene Complexes

We report the synthesis and characterisation of a series of rare-earth mesoionic carbene complexes, [RE{N(SiMe₃)₂}₃{CN(Me)C(Me)N(Me)CH}] ( 3RE , RE=Sc, Ce, Pr, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu), greatly expanding the limited library of f-block mesoionic carbene complexes. These complexes were prepared by treatment of the parent RE-triamides with an N-heterocyclic olefin (NHO), where an NHO backbone proton undergoes a formal 1,4-proton migration to the NHO-methylene group. For all RE(III) metals, as expected, quantum chemical calculations suggest only a σ-component to the metal−carbene bonding, in contrast to a previously reported uranium(III) congener where the 5f³ metal engages in a weak π-back-bond to the MIC. All complexes were characterised by static variable-temperature magnetic measurements, and dynamic magnetic measurements reveal that 3Dy and 3Er are field-induced single-molecule magnets (SMMs), with U_eff energy barriers of 35 and 128 K, respectively. Complex 3Dy is, as expected, a poorly performing SMM, but conversely 3Er performs unexpectedly well.     

Narrow Parameter Windows and Analogues of Contextual Noise in Nonlinear Psychophysics

The dependency of outputs of three types; real, imaginary and cross-entropy mappings, all over a lattice of pixels, each of which is generated by a complex cubic polynomial nonlinear trajectory, is examined as a function of the cross-coupling between any pixel and its neighbourhood. It is found that the system can transmit information efficiently only within a narrow parameter window, which represents an optimum level of diffusion in space and reconfiguration in time. The topology of stimulus patterns, which are open or closed in their contours, can have a critical effect on the distribution of information in the system's output. Signals which are not processed within a limited temporal and parameter window are eventually degenerated and lost. There are phenomena associated with edge-of-chaos at some stages in the system. Problems of predictability when second-order stochastic noise is superimposed on the trajectory's parameters are explored, and differences from signal detection models are noted.     

Responses to Constrained Stimulus Sequences in Nonlinear Psychophysics

Generic models used in nonlinear psychophysical dynamics (NPD) have been extensively explored for their capacity to simulate both local singular phenomena and non-monotonic response functions. Internal parameters representing a form of system sensitivity and secondary recursive activity can interact when very low stimulation operates on the gain controlling the evolution of response trajectories, when these trajectories evolve either singly or when chained. Ways in which an existing NPD model can, without change of structure, incorporate naturalistic processes of feedback and stimulus constraint are illustrated. Stimuli-response pairs presented in long closely spaced sequences may appear to be created by a diversity of cognitive strategies, but this assumption is not necessary if nonlinear dynamics are involved. The total system may then resemble the convolution of two fast/slow trajectories. Cusp catastrophe-like sequences can be induced. Nonparametric bases for making statistical comparisons between theory and data, when both are in time series form, are given.     

Titanium-salen complexes as initiators for the ring opening polymerisation of rac-lactide

A family of bis(iso-propoxide) titanium(IV) complexes supported by tetradentate Schiff base (salen) ligands has been synthesised and characterised, including a structural determination of N,N'-bis(6'-methylenimino-2',4'-di-tert-butylphenoxy)cyclohexyl-(1R,2R)-diamino titanium(IV) bis(iso-propoxide). Their suitability for initiating the ring-opening polymerisation of rac-lactide has been investigated. Polymerisation activities are shown to correlate with the electronic properties of the substituents within the salen ligand. In contrast to aluminium-salen initiators, electron-withdrawing substituents on the Schiff base ligand have a detrimental influence upon polymerisation activities, whereas the use of electron-donating alkoxy-functionalized ligands has allowed the highest recorded activity to date for a titanium-based initiator.