Temporal difference models describe higher-order learning in humans.

The ability to use environmental stimuli to predict impending harm is critical for survival. Such predictions should be available as early as they are reliable. In pavlovian conditioning, chains of successively earlier predictors are studied in terms of higher-order relationships, and have inspired computational theories such as temporal difference learning. However, there is at present no adequate neurobiological account of how this learning occurs. Here, in a functional magnetic resonance imaging (fMRI) study of higher-order aversive conditioning, we describe a key computational strategy that humans use to learn predictions about pain. We show that neural activity in the ventral striatum and the anterior insula displays a marked correspondence to the signals for sequential learning predicted by temporal difference models. This result reveals a flexible aversive learning process ideally suited to the changing and uncertain nature of real-world environments. Taken with existing data on reward learning, our results suggest a critical role for the ventral striatum in integrating complex appetitive and aversive predictions to coordinate behaviour.

An investigation of higher-order multi-objective optimisation for 3D aerodynamic shape design

We investigate the performance of different variants of a suitably tailored Tabu Search optimisation algorithm on a higher-order design problem. We consider four objective func- tions to describe the performance of a compressor stator row, subject to a number of equality and inequality constraints. The same design problem has been previously in- vestigated through single-, bi- and three-objective optimisation studies. However, in this study we explore the capabilities of enhanced variants of our Multi-objective Tabu Search (MOTS) optimisation algorithm in the context of detailed 3D aerodynamic shape design. It is shown that with these enhancements to the local search of the MOTS algorithm we can achieve a rapid exploration of complicated design spaces, but there is a trade-off be- tween speed and the quality of the trade-off surface found. Rapidly explored design spaces reveal the extremes of the objective functions, but the compromise optimum areas are not very well explored. However, there are ways to adapt the behaviour of the optimiser and maintain both a very efficient rate of progress towards the global optimum Pareto front and a healthy number of design configurations lying on the trade-off surface and exploring the compromise optimum regions. These compromise solutions almost always represent the best qualitative balance between the objectives under consideration. Such enhancements to the effectiveness of design space exploration make engineering design optimisation with multiple objectives and robustness criteria ever more practicable and attractive for modern advanced engineering design. Finally, new research questions are addressed that highlight the trade-offs between intelligence in optimisation algorithms and acquisition of qualita- tive information through computational engineering design processes that reveal patterns and relations between design parameters and objective functions, but also speed versus optimum quality. © 2012 AIAA.

Aeroacoustic source measurement methods for characterizing the sound generated by ducted flow devices with higher-order modes.

The International Organization for Standardization (ISO) method 5136 is widely used in industry and academia to determine the sound power radiated into a duct by fans and other flow devices. The method involves placing the device at the center of a long cylindrical duct with anechoic terminations at each end to eliminate reflections. A single off-axis microphone is used on the inlet and outlet sides that can theoretically capture the plane-wave mode amplitudes but this does not provide enough information to fully account for higher-order modes. In this study, the "two-port" source model is formulated to include higher-order modes and applied for the first three modes. This requires six independent surface pressure measurements on each side or "port." The resulting experimental set-up is much shorter than the ISO rig and does not require anechoic terminations. An array of six external loudspeaker sources is used to characterize the passive part of the two-port model and the set-up provides a framework to account for transmission of higher-order modes through a fan. The relative importance of the higher-order modes has been considered and their effect on inaccuracies when using the ISO method to find source sound power has been analyzed.

Finite Element studies on indentation size effect using a higher order strain gradient theory

In this work, a Finite Element implementation of a higher order strain gradient theory (due to Fleck and Hutchinson, 2001) has been used within the framework of large deformation elasto-viscoplasticity to study the indentation of metals with indenters of various geometries. Of particular interest is the indentation size effect (ISE) commonly observed in experiments where the hardness of a range of materials is found to be significantly higher at small depths of indentation but reduce to a lower, constant value at larger depths. That the ISE can be explained by strain gradient plasticity is well known but this work aims to qualitatively compare a gamut of experimental observations on this effect with predictions from a higher order strain gradient theory. Results indicate that many of the experimental observations are qualitatively borne out by our simulations. However, areas exist where conflicting experimental results make assessment of numerical predictions difficult. © 2012 Elsevier Ltd. All rights reserved.

a higher-order duration calculus and its completeness

National Natural Science Foundation of China; Public Administration and Civil Service Bureau of Macau SAR; Companhia de Telecomunicacoes de Macau S.A.R.L.; Macau SAR Government Tourist Office

Bimolecular quadruplexes and their transitions to higher-order molecular structures detected by ESI-FTICR-MS

Four individual quadruplexes, which are self-assembled in ammonium acetate solution from telomeric sequences of closely related DNA strands - d(G(4)T(4)G(4)), d(G(3)T(4)G(4)), d(G(3)T(4)G(3)), and d(G(4)T(4)G(3)) - have been detected in the gas phase using electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICR-MS). The bimolecular quadruplexes associate with the same number of NH4+ in the gas phase as NMR shows that they do in solution. The quadruplex structures formed in solution are maintained in the gas phase. Furthermore, the mass spectra show that the bimolecular quadruplexes generated by the strands d(G(3)T(4)G(3)) and d(G(4)T(4)G(3)) are unstable, being converted into trimolecular and tetramolecular structures with increasing concentrations of NH4+ in the solution. Circular dichroism (CD) spectra reveal structural changes during the process of strand stoichiometric transitions, in which the relative orientation of strands in the quadruplexes changes from an antiparallel to a parallel arrangement. Such changes were observed for the strand d(G(4)T(4)G(3)), but not for the strand d(G(3)T(4)G(3)). The present work provides a significant insight into the formation of various DNA quadruplexes, especially the higher-order species.

Higher-order Boussinesq-type equations for interfacial waves in a two-fluid system

Interfacial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa's results (1999). The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. (1991) and Schaffer and Madsen (1995a). It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer (1998). By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa's (1999) results, and the applicable scope of water depth is deeper.

Higher order response of nonlinear composite in external AC electric field

The fifth-order effective nonlinear responses at fundament frequency and higher-order harmonics are given for nonlinear composites, which obey a current-field relation of the form J = sigmaE + x\E\(2) E, if a sinusoidal alternating current (AC) external field with finite frequency omega is applied. As two examples, we have investigated the cylinder and spherical inclusion embedded in a host and, for larger volume fraction, also derived the formulae of effective nonlinear responses at higher-order harmonics by the aid of the general effective response definition. Furthermore, the relationships between effective nonlinear responses at harmonics are given. (C) 2003 Elsevier Science B.V. All rights reserved.